`BookProof.Complexification.Cx.cxConj_comm_cxMap` (m : W →L[ℝ] W) (x : Cx W) : cxConj (cxMap m x) = cxMap m (cxConj x)

Proved

BookProof.Complexification.Cx.cxConj_comm_cxMap

by leonardopedro · Oct 10, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from Complexification.

BookProof.Complexification.Cx.cxConj_comm_cxMap (m : W →L[ℝ] W) (x : Cx W) : cxConj (cxMap m x) = cxMap m (cxConj x)

Formalization note: Lean 4 identifier BookProof.Complexification.Cx.cxConj_comm_cxMap.

Preamble

-- Generated from Complexification.lean — theorem BookProof.Complexification.Cx.cxConj_comm_cxMap
import Mathlib
import Definitions.Def_Complexification
import Definitions.Def_ChapterQgOuterFockCoreFL
open BookProof.QgOuterFockCoreFL
open BookProof.QgOuterFockCoreFL.CoreData
open BookProof.Complexification
open BookProof.Complexification


open scoped RealInnerProductSpace
open RCLike


set_option linter.unusedSectionVars false

variable {W : Type*} [NormedAddCommGroup W] [InnerProductSpace ℝ W]

Formal statement

theorem BookProof.Complexification.Cx.cxConj_comm_cxMap (m : W →L[ℝ] W) (x : Cx W) :
    cxConj (cxMap m x) = cxMap m (cxConj x) := by sorry

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